What is the general solution for tan^2(x)+3tan(x)+1=0 ?

The general solution for tan^2(x)+3tan(x)+1=0 is x=-0.36486…+pin,x=-1.20593…+pin

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tan^2(x)+3tan(x)+1=0

tan^{2} (x) + 3 tan (x) + 1 = 0

x = - 0.36486 \dots + πn, x = - 1.20593 \dots + πn

Solution steps

tan^{2} (x) + 3 tan (x) + 1 = 0

Solve by substitution

tan (x) = \frac{- 3 + 5}{2}, tan (x) = \frac{- 3 - 5}{2}

tan (x) = \frac{- 3 + 5}{2} : x = arctan (\frac{- 3 + 5}{2}) + πn

tan (x) = \frac{- 3 - 5}{2} : x = arctan (\frac{- 3 - 5}{2}) + πn

Combine all the solutions

x = arctan (\frac{- 3 + 5}{2}) + πn, x = arctan (\frac{- 3 - 5}{2}) + πn

Show solutions in decimal form

x = - 0.36486 \dots + πn, x = - 1.20593 \dots + πn

csc (2 x) = 2, 0 \leq x < 2 π

sin (x) + cos (x) = 1.2

30 cos (30 x) + 14 = - 16

x, cot (- x) cos (- x) + sin (- x) = - \frac{1}{f}

cos (x) = - \frac{2}{3}

What is the general solution for tan^2(x)+3tan(x)+1=0 ?
The general solution for tan^2(x)+3tan(x)+1=0 is x=-0.36486…+pin,x=-1.20593…+pin